Kyle Broder

collaborators

5 papers

math.DG2026

Curvature of hyperbolic complex manifolds

Kyle Broder, HervÃ© Gaussier

The article addresses the construction and geography of negatively curved metrics on hyperbolic complex manifolds. We introduce a mechanism for constructing complete KÃ¤hler metric…

math.DG2026

Cohomogeneity-one Einstein metrics on closed $4$ -manifolds

Kyle Broder

We classify the Einstein metrics on closed 4-manifolds whose isometry group has dimension at least 3. Consequently, we show that the cohomogeneity-one Einstein metrics on a closed…

math.AG2026

Weakly Special Manifolds with no rational curves

Kyle Broder, FrÃ©dÃ©ric Campana

Assuming the abundance conjecture and the existence of a Zariski dense set of rational curves on terminal Calabi--Yau varieties, we show that a complex projective weakly special ma…

math.DG2026

Holomorphic $p$ -Contact and $s$ -Symplectic Line Bundles

Kyle Broder, Dan Popovici

We generalise the notions of scalar-valued holomorphic $p$ -contact and $s$ -symplectic structures introduced recently on compact complex manifolds by the second-named author jointly…

math.DG2025

Hyperbolicity and Schwarz Lemmas in Calibrated Geometry

Kyle Broder, Anton Iliashenko, Jesse Madnick

This paper has two main objectives. First, for an arbitrary calibrated manifold $(X, I ¨ )$ , we define notions of $R_{I ¨} $ -hyperbolicity and $I ¨ $ -hyperbolicity, which respectively gener…

Curvature of hyperbolic complex manifolds

Cohomogeneity-one Einstein metrics on closed 4-manifolds

Weakly Special Manifolds with no rational curves

Holomorphic p-Contact and s-Symplectic Line Bundles

Hyperbolicity and Schwarz Lemmas in Calibrated Geometry

Cohomogeneity-one Einstein metrics on closed $4$ -manifolds

Holomorphic $p$ -Contact and $s$ -Symplectic Line Bundles